You can actually do it on a much shorter time scale, depending on the species in question. A Soviet scientist in the 50s started it with foxes and had noticeable results by the 4th generation, less than 2 decades later.

The real catch here is in the semantics, defining your terms and expectations. How much genetic drift you're aiming for, and what traits you select, what results are functionally "good enough", etc...

In this example, we probably don't need fully domesticated animals, some tamed generations should be good enough.